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Description

Since the introduction of the idea of adding parallelism to time integration in the seminal work of Nievergelt in 1964, various approaches for parallel-in-time integration have been explored. One of these approaches is applying multigrid to the time dimension, resulting in the multigrid-reduction-in-time (MGRIT) algorithm by Falgout et al. The corresponding open source code XBraid is flexible, allowing for a variety of time stepping, relaxation, and temporal coarsening options. It was recently shown in Bolten et al. that the time-parallel expansion of spectral deferred corrections methods, the Parallel Full Approximation Scheme in Space and Time (PFASST) algorithm by Emmett and Minion, can be described as a multigrid-in-time method under certain assumptions. In this talk, we discuss approaches for incorporating aspects of PFASST and multigrid-based parallel-in-time methods into XBraid.